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PROBLEM TO BE SOLVED : To accelerate the conversion of CO2 into methane by reaction with H2 by subjecting a precursor made of an amorphous alloy contg. of = specified at.% Zr and specified at.% a rare earth element to oxidant-reduction treatment. SOLUTION : A precursor made of an amorphous alloy consisting of =20at.% Zr and >5 to <=15at.% one or more kinds of rare earth elements selected from among Y, La, Ce, Nd, Sm, Gd, Tb and Dy and the balance essentially Co and/or Ni is subjected to oxidation-reduction treatment to obtain the objective amorphous alloy catalyst. When this catalyst is used, the conversion of CO2 into methane by reaction with H2 under atmospheric pressure can be accelerated and a large amt. of CO2 can be converted into methane at a high rate.